According to ISO 26262 (the international standard on functional safety for automotive industry), the functional safety should be considered during the whole automotive systems life cycle from the design phase throughout the production phase. In order to satisfy the standard, the automotive and related industry needs to take appropriate actions while carrying out a variety of development activities. This paper presents an approach to coping with the standard. Analyzing the standard indicates that the safety issues of the automotive systems should be handled with a system's view whereas the conventional approach to solving the issues has been practiced with focus on the component's level. The aforementioned system's view implies that the functional safety shall be incorporated in the system design from both the system's life-cycle view and the hierarchical view for the structure. In light of this, the systems engineering framework can be quite appropriate in the functional safety development and thus has been taken in this paper as a problem solving approach. Of various design issues, the analysis and verification of the safety requirements for functional safety is a key study subject of the paper. Note, in particular, that the conventional FMEA (failure mode effects analysis) and FTA (fault tree analysis) methods seem to be partly relying on the insufficient experience and knowledge of the engineers. To improve this, a systematic method is studied here and the result is applied in the design of an ABS braking system as a case study.